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Differential Geometry - Period 1+2
Social Sciences & Humanities Program
Amsterdam, Netherlands
Dates: 8/16/24 - 12/21/24
Differential Geometry - Period 1+2
OVERVIEW
CEA CAPA Partner Institution: Vrije Universiteit Amsterdam
Location: Amsterdam, Netherlands
Primary Subject Area: Mathematics
Instruction in: English
Course Code: X_400631
Transcript Source: Partner Institution
Course Details: Level 400
Recommended Semester Credits: 3
Contact Hours: 84
Prerequisites: Single Variable and Multi Variable Calculus, Mathematical Analysis, Linear Algebra.
DESCRIPTION
This course is an introduction to the theory of manifolds. Apart from giving the most relevant definitions from differential geometry (manifolds, vector bundles and differential forms), we make short excursions to Riemannian geometry (Riemannian metrics), dynamical systems (flows of vector fields), as well as to algebraic topology (fundamental group and de Rham cohomology). More precisely, the subject list includes:
- Submanifolds, manifolds, tangent vectors
- Smooth maps (between manifolds), differential,immersions/submersions/embeddings
- Vector fields and their flows, Lie bracket, Lie groups
- Vector bundles, tangent bundles, tensor products, sections
- Riemannian metrics, distances on Riemannian manifolds
- Differential forms, pullbacks, exterior derivative
- Stokes' Theorem and De Rham cohomology
- Fundamental group and outlook towards algebraic topology
Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
- Submanifolds, manifolds, tangent vectors
- Smooth maps (between manifolds), differential,immersions/submersions/embeddings
- Vector fields and their flows, Lie bracket, Lie groups
- Vector bundles, tangent bundles, tensor products, sections
- Riemannian metrics, distances on Riemannian manifolds
- Differential forms, pullbacks, exterior derivative
- Stokes' Theorem and De Rham cohomology
- Fundamental group and outlook towards algebraic topology
Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.